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this is one of the questions that came up in my iGCSE math exam and i was just woundering if anyone can anser it because i really didn't know what to do. :)
two spheres fit exactly inside a cilinder so the space left in the cylinder with them inside it is 125/6pi
find the radius of the cylinder?
volume of cylinder = 4 x r cubed x pi (in this case because the length is the same as 4xr )
volume of both spheres = 8/3 x r cubed x pi
cylinder - spheres = 125/6 x pi
We can now divide both sides by pi and then by 4 to get
r cubed- 2/3 r cubed = 125/24 or 1/3 r cubed = 125/24
which means if we then times both sides by 3 we will get r cubed = 125/8
Finnaly if we cube root 125/8 it will give us the radius which is 2.5
Modified once, last modified by Ragnaros the Firelord on Wed 23rd May, 2012 @ 17:38
I had spent half an hour writing a longer method out but my internet crashed XD so i lost all of my workings.
The difficulty in this question is too know that the volume of a sphere is 4/3 x pi x r cubed, also understading that if the spheres fit exactly inside the cylinder they share the same radius
and being able to put it into a formula and rearanging it for r, where r is the radius.
hope this helps it took me a bit of time to do as well ^^
Modified twice, last modified by Ragnaros the Firelord on Wed 23rd May, 2012 @ 17:29
Thanks this was really helpful. :)
I got stuck trying to rearnge the formulas to get r on its own.